Finite Group Databasebeta

← C151×#23899 #50328824

Subgroups — C151×#23899 #50328824

Order 38656.

1672 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1672 conjugacy classes of subgroups — too many to draw. Only its 282 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3486×C151C212yesmaximal, complemented
2#3020×C151C214yesmaximal, complemented
3#2010×C151C214yesmaximal, complemented
4#1912×C151C214yesmaximal, complemented
5#1784×C151C211yesmaximal, characteristic, complemented
6C2×2−1+4×C151C2212yes—
7C23×Q8×C151C2211yescharacteristic
8#575×C151C2214yes—
9D4×Q8×C151—28no—
10#548×C151—28no—
11#536×C151—24no—
12#536×C151C2214yes—
13#525×C151—24no—
14#525×C151C2214yes—
15#519×C151C2212yes—
16#456×C151—28no—
17#454×C151—28no—
18#421×C151C2218yes—
19C2×#101×C151C2214yes—
20#407×C151C2212yes—
21H(3,ℤ/4)×C151C2214yes—
222−1+4×C151—28no—
232−1+4×C151—44no—
24C2×#41×C151—24no—
25C2×#41×C151—24no—
26C2×#41×C151C2314yes—
27C22×Q8×C151—28no—
28C22×Q8×C151—24no—
29C22×Q8×C151—42no—
30C22×Q8×C151D412yes—
31C22×Q8×C151C2312yes—
32C23×C4×C151D412yes—
33C23×C4×C151C2311yescharacteristic
34#137×C151—28no—
35AGL(1,ℤ/8)×C151—28no—
36#135×C151—44no—
37C2×M16×C151C2314yes—
38C4⋊Q8×C151—28no—
39C4⋊Q8×C151D418yescomplemented
40#124×C151—28no—
41#124×C151D418yescomplemented
42#123×C151—28no—
43#123×C151—24no—
44C22⋊Q8×C151—28no—
45C22⋊Q8×C151—216no—
46C22⋊Q8×C151—24no—
47C22⋊Q8×C151—28no—
48#121×C151—28no—
49#121×C151—24no—
50#120×C151—24no—
51C4×Q8×C151—28no—
52C4×D4×C151—216no—
53C4×D4×C151—28no—
54#117×C151—24no—
55#117×C151C2314yes—
56#104×C151—216no—
57#101×C151—28no—
58C22⋊C8×C151—42no—
59C24×C151C2×D411yescharacteristic
60#41×C151—28no—
61#41×C151—28no—
62#41×C151—48no—
63#41×C151—416no—
64#41×C151—48no—
65C2×Q8×C151—24no—
66C2×Q8×C151—28no—
67C2×Q8×C151—24no—
68C2×Q8×C151—24no—
69C2×Q8×C151—42no—
70C2×Q8×C151—416no—
71C2×Q8×C151—416no—
72C2×Q8×C151C2×D414yes—
73C2×Q8×C151C2×D418yes—
74C2×D4×C151—28no—
75C2×D4×C151—24no—
76C2×D4×C151—24no—
77C2×D4×C151C2×D414yes—
78C22×C4×C151—28no—
79C22×C4×C151—28no—
80C22×C4×C151—24no—
81C22×C4×C151—24no—
82C22×C4×C151—22no—
83C22×C4×C151—42no—
84C22×C4×C151C2×D411yescharacteristic
85C22×C4×C151C2×D414yes—
86C22×C4×C151C2411yescharacteristic
87Q16×C151—44no—
88SD16×C151—48no—
89D8×C151—44no—
90M16×C151—28no—
91C2×C8×C151—24no—
92C4⋊C4×C151—28no—
93C4⋊C4×C151—28no—
94C4⋊C4×C151—216no—
95C4⋊C4×C151—24no—
96C22⋊C4×C151—28no—
97C22⋊C4×C151—28no—
98C22⋊C4×C151—24no—
99C22⋊C4×C151—216no—
100C42×C151—28no—
101C42×C151C2×D418yes—
102C23×C151—22no—
103C23×C151—21no—
104C23×C151—24no—
105C23×C151—42no—
106C23×C151C22×D411yescharacteristic
107Q8×C151—216no—
108Q8×C151—28no—
109Q8×C151—48no—
110Q8×C151—48no—
111D4×C151—28no—
112D4×C151—48no—
113D4×C151—416no—
114D4×C151—44no—
115D4×C151—44no—
116C2×C4×C151—24no—
117C2×C4×C151—24no—
118C2×C4×C151—22no—
119C2×C4×C151—24no—
120C2×C4×C151—28no—
121C2×C4×C151—21no—
122C2×C4×C151—48no—
123C2×C4×C151—416no—
124C2×C4×C151—44no—
125C2×C4×C151—48no—
126C2×C4×C151#12018yes—
127C2×C4×C151C22×D414yes—
128C2×C4×C151H(5,𝔽2)12yes—
129C8×C151—44no—
130C22×C151—24no—
131C22×C151—22no—
132C22×C151—41no—
133C22×C151—42no—
134C22×C151—41no—
135C22×C151—48no—
136C22×C151—41no—
137C22×C151—44no—
138C22×C151C2×#12012yes—
139C22×C151#53411yescharacteristic
140C4×C151—28no—
141C4×C151—48no—
142C4×C151—41no—
143C4×C151—44no—
144C4×C151D4214yes—
145C2×C151—22no—
146C2×C151—21no—
147C2×C151—42no—
148C2×C151—84no—
149C2×C151#240311yescharacteristic
150#23899C15111yesmaximal, characteristic, direct product factor, Sylow
151C151#2389911yescharacteristic, direct product factor, Sylow
152#3486C2×C15112yescomplemented
153#3020C2×C15114yescomplemented
154#2010C2×C15114yescomplemented
155#1912C2×C15114yescomplemented
156#1784C2×C15111yescharacteristic, complemented
157C2×2−1+4C22×C15112yes—
158C23×Q8C22×C15111yescharacteristic
159#575C22×C15114yes—
160D4×Q8—28no—
161#548—28no—
162#536—24no—
163#536C22×C15114yes—
164#525—24no—
165#525C22×C15114yes—
166#519C22×C15112yes—
167#456—28no—
168#454—28no—
169#421C22×C15118yes—
170C2×#101C22×C15114yes—
171#407C22×C15112yes—
172H(3,ℤ/4)C22×C15114yes—
1732−1+4—28no—
1742−1+4—44no—
175C2×#41—24no—
176C2×#41—24no—
177C2×#41C23×C15114yes—
178C22×Q8—28no—
179C22×Q8—24no—
180C22×Q8—42no—
181C22×Q8D4×C15112yes—
182C22×Q8C23×C15112yes—
183C23×C4D4×C15112yes—
184C23×C4C23×C15111yescharacteristic
185#137—28no—
186AGL(1,ℤ/8)—28no—
187#135—44no—
188C2×M16C23×C15114yes—
189C4⋊Q8—28no—
190C4⋊Q8D4×C15118yescomplemented
191#124—28no—
192#124D4×C15118yescomplemented
193#123—28no—
194#123—24no—
195C22⋊Q8—28no—
196C22⋊Q8—216no—
197C22⋊Q8—24no—
198C22⋊Q8—28no—
199#121—28no—
200#121—24no—
201#120—24no—
202C4×Q8—28no—
203C4×D4—216no—
204C4×D4—28no—
205#117—24no—
206#117C23×C15114yes—
207#104—216no—
208#101—28no—
209C22⋊C8—42no—
210C24C2×D4×C15111yescharacteristic
211#41—28no—
212#41—28no—
213#41—48no—
214#41—416no—
215#41—48no—
216C2×Q8—24no—
217C2×Q8—28no—
218C2×Q8—24no—
219C2×Q8—24no—
220C2×Q8—42no—
221C2×Q8—416no—
222C2×Q8—416no—
223C2×Q8C2×D4×C15114yes—
224C2×Q8C2×D4×C15118yes—
225C2×D4—28no—
226C2×D4—24no—
227C2×D4—24no—
228C2×D4C2×D4×C15114yes—
229C22×C4—28no—
230C22×C4—28no—
231C22×C4—24no—
232C22×C4—24no—
233C22×C4—22no—
234C22×C4—42no—
235C22×C4C2×D4×C15111yescharacteristic
236C22×C4C2×D4×C15114yes—
237C22×C4C24×C15111yescharacteristic
238Q16—44no—
239SD16—48no—
240D8—44no—
241M16—28no—
242C2×C8—24no—
243C4⋊C4—28no—
244C4⋊C4—28no—
245C4⋊C4—216no—
246C4⋊C4—24no—
247C22⋊C4—28no—
248C22⋊C4—28no—
249C22⋊C4—24no—
250C22⋊C4—216no—
251C42—28no—
252C42C2×D4×C15118yes—
253C23—22no—
254C23—21no—
255C23—24no—
256C23—42no—
257C23C22×D4×C15111yescharacteristic
258Q8—216no—
259Q8—28no—
260Q8—48no—
261Q8—48no—
262D4—28no—
263D4—48no—
264D4—416no—
265D4—44no—
266D4—44no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—28no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—21no—
273C2×C4—48no—
274C2×C4—416no—
275C2×C4—44no—
276C2×C4—48no—
277C2×C4#120×C15118yes—
278C2×C4C22×D4×C15114yes—
279C2×C4H(5,𝔽2)×C15112yes—
280C8—44no—
281C22—24no—
282C22—22no—
283C22—41no—
284C22—42no—
285C22—41no—
286C22—48no—
287C22—41no—
288C22—44no—
289C22C2×#120×C15112yes—
290C22#534×C15111yescharacteristic
291C4—28no—
292C4—48no—
293C4—41no—
294C4—44no—
295C4D42×C15114yes—
296C2—22no—
297C2—21no—
298C2—42no—
299C2—84no—
300C2#2403×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#2403
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C22×C4×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3486×C151C2semidirect
2. #3020×C151C2semidirect
3. #2010×C151C2semidirect
4. #1912×C151C2semidirect
5. #1784×C151C2semidirect
39. C4⋊Q8×C151D4semidirect
41. #124×C151D4semidirect
150. #23899C151direct (N × H)
151. C151#23899direct (N × H)
152. #3486C2×C151semidirect
153. #3020C2×C151semidirect
154. #2010C2×C151semidirect
155. #1912C2×C151semidirect
156. #1784C2×C151semidirect
190. C4⋊Q8D4×C151semidirect
192. #124D4×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#3486×C1512
#3020×C1512
#2010×C1512
#1912×C1512
#1784×C1512
#23899151